Question

   

A certain genetic characteristic of a particular plant can appear in one of three forms (phenotypes). A researcher has developed a theory, according to which the hypothesized proportions are p₁ = 0.25, p₂ = 0.50, and p₃ = 0.25. A random sample of 200 plants yields X² = 4.88.

(a)

Carry out a test of the null hypothesis that the theory is correct, using level of significance α = 0.05. (Use technology. Round your answer to four decimal places.)

P-value =

State the conclusion in the problem context.

Fail to reject H₀. There is convincing evidence that the researcher's theory is incorrect.Reject H₀. There is not convincing evidence that the researcher's theory is incorrect.    Fail to reject H₀. There is not convincing evidence that the researcher's theory is incorrect.Reject H₀. There is convincing evidence that the researcher's theory is incorrect.

(b)

Suppose that a random sample of 300 plants had resulted in the same value of X². How would your analysis and conclusion differ from those in part (a)?

The previous analysis did not yield a significant result and the null hypothesis failed to be rejected. The new analysis would yield a significant result and the null hypothesis would be rejected.The analysis and conclusion would not change.    The previous analysis yielded a significant result and the null hypothesis was rejected. The new analysis would not yield a significant result and the null hypothesis would fail to be rejected.

   

7.

[–/4 Points]DETAILSPECKSTAT2 14.E.015.MI.

MY NOTES

PRACTICE ANOTHER

A particular article reported the accompanying data on phenotypes resulting from crossing tall cut-leaf tomatoes with dwarf potato-leaf tomatoes. There are four possible phenotypes: (1) tall cut-leaf, (2) tall potato-leaf, (3) dwarf cut-leaf, and (4) dwarf potato-leaf.

	Phenotype
	1	2	3	4
Frequency	927	289	291	105

Mendel's laws of inheritance imply that p₁ =

9

16

, p₂ =

3

16

, p₃ =

3

16

, and p₄ =

1

16

. Are the data from this experiment consistent with Mendel's laws? Use a 0.01 significance level. (Assume that the sample is representative of all such tomato plants.)

State the appropriate null and alternative hypotheses.

H₀: p₁ ≠

9

16

, p₂ ≠

3

16

, p₃ ≠

3

16

, p₄ ≠

1

16

H_a: H₀ is not true.

H₀: p₁ =

9

16

, p₂ =

3

16

, p₃ =

3

16

, p₄ =

1

16

H_a: H₀ is not true.

    H₀: p₁ =

1

4

, p₂ =

1

4

, p₃ =

1

4

, p₄ =

1

4

H_a: H₀ is not true.

H₀: p₁ = 927, p₂ = 289, p₃ = 291, p₄ = 105

H_a: H₀ is not true.

H₀: p₁ ≠ 927, p₂ ≠ 289, p₃ ≠ 291, p₄ ≠ 105

H_a: H₀ is not true.

Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.)

X²=P-value=

State the conclusion in the problem context.

Fail to reject H₀. There is not convincing evidence that the data from this experiment are not consistent with Mendel's laws.Fail to reject H₀. There is convincing evidence that the data from this experiment are not consistent with Mendel's laws.    Reject H₀. There is not convincing evidence that the data from this experiment are not consistent with Mendel's laws.

Answer 1